Coulomb Interaction Induced Gap in an Al/SiO2/Si:P tunnelling Device

Abstract

I. Introduction

Silicon is like to be the best known semiconductor material. Despite its poor mobility and carrier concentration, it has been extensively used in the semiconductor industry owing to its simple doping processes and price advantage. Specially, doping increases the carrier density in the silicon, causing several intriguing phenomena, such as a semiconductor (insulator) to metal transition (MIT) [1]. As the temperature decreases, interactions caused by the increased carrier density are no longer negligible. Such behavior is not only useful from an industrial point of view but also presents an interesting topic in condensed matter physics.

In this work, we utilize tunnelling spectroscopy measurements at ultra-low temperature in an effort to investigate intriguing phenomena such as an abnormal gap induced by Coulomb interaction. We used a tunnelling device with a heavily doped Si:P and superconducting Al electrode.

II. Experiments

Al electrodes and the thermally grown SiO₂ tunnelling barrier used here were fabricated on phosphorus-doped silicon (Si:P) substrates (see Fig. 1(a)). The doping concentration of the Si:P exceeds 10¹⁹/cm³ in all cases. A native oxide layer on Si:P was removed using HF and the SiO₂ tunnelling barrier was directly grown on the Si:P using a tube furnace. A shadow mask was used to fabricate the Al electrodes with a thermal evaporator. Each electrode was 200 nm thick and had a diameter of 500 μm.

Figure 1

(a) Schematic of an Al/SiO2/Si:P tunnelling device. (b) Mounted samples on the sample holder of a 3He/4He dilution system.

Ultra-low temperature transport characteristics were investigated using a ³He/⁴He dilution system. Figure 1(b) shows mounted samples on the holder. Silver paste was used to fix the sample, and a ground pad was connected. In addition, 25 μm Au wires were carefully bonded using a bonding machine. Special care was taken to avoid damage to the SiO₂ tunnelling layer. Up to 1800 gauss was applied using a superconducting magnet at a base temperature of 30 mK. All transport measurements were done at NEC in the Tsukuba Lab in Japan.

Tunnelling spectroscopy was conducted in order to observe the tunnelling DOS near the Fermi level of Si:P. This measurement allows us to investigate many condensed matter phenomena by measuring the DOS directly. The first-order derivative of the tunnelling current is proportional to the DOS [2]. The tunnelling current is given by the equation below:

Because the Al electrode has a superconducting gap of approximately 0.2 mV, the tunnelling conductance between the superconducting gap of Al is directly proportional to the tunnelling DOS of the Si:P. Thus, Eq. (1) becomes

This can also be applied to other metals which have a flat DOS structure in the vicinity of the Fermi level.

III. Results and Discussion

The temperature-dependent conductance curves of the sample are shown in Fig. 2(a). In this case, the well-known superconducting gap of the Al electrode was observed below 1.1 K, as expected (marked with arrows). As the temperature was decreased to less than 130 mK, another gap started to develop in the vicinity of the zero bias conductance. The observed gap survived at more than 1800 gauss, whereas the superconducting gap was completely suppressed above 100 gauss, as shown in Fig. 2(b). The observed conductance characteristics imply that the observed gap is independent of the applied magnetic fields.

Figure 2

(a) Temperature and (b) magnetic field dependences of the tunnelling conductance in an Al/SiO2/Si:P tunnelling device.

Figure 3(a) shows the conductance curve (dI/dV) versus V^0.5. The relationship between the conductance and the bias voltage is well described by the typical tunnelling conductance behavior for a Coulomb gap, as follows [3–6],

Figure 3

(a) Comparison of the measured conductance versus V0.5 in an Al/SiO2/Si:P device. The tunnelling conductance is symmetric with respect to the bias origin. (b) Logarithm of the zero bias conductance ...

which is caused by long-range Coulomb interactions in disordered metals. This observation suggests that Si:P can be regarded as a disordered metal [4–6].

A Coulomb gap in the metallic region of a doped semiconductor leads to variable-range hopping (VRH) conductivity. Therefore, the temperature-induced smearing of the Coulomb gap can be determined by the following equation [5–7]:

This formula is fundamentally in good agreement with our data (see Fig. 3(b)). As the temperature decreases from ~ 130 mK, the zero bias conductance decreases following the T^-0.5 behaviour (see Fig. 3(b)), suggesting that the Coulomb gap appears below 130 mK. This is consistent with the data in Fig. 2(a).

IV. Conclusions

A Al/SiO₂/Si:P tunnelling device was prepared by means of thermal annealing and evaporating techniques. An intriguing gap was found at highly phosphorus-doped Si below ~ 130mK via tunnelling spectroscopy. The results from temperature- and magnetic-field-dependent conductance measurements showed that the observed gap is induced by long-range coulomb interaction between localized states. Phosphorus-doped silicon has been studied for decades only near the metal-insulator transition boundary. Our findings in the totally degenerated region suggest the possibility for additional discoveries beyond the boundary of MIT in Si:P.

Acknowledgements

This project was supported by the National Research Foundation (NRF) of Korea (Grant Nos. 2015R1A2A 2A01004782 and 2016R1A6A1A03012877).

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